Finite Group DatabasebetaFinite Group Databasebeta| order | 22660 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C11⋊C5×Dic103 |
| unambiguous semidirect product | C103⋊(C4×C11⋊C5) |
| unambiguous semidirect product | (C11×Dic103)⋊C5 |
| derived, Hall | C11×C103 ⋊ C4×C5 |
| Hall | C11⋊C5×C103 ⋊ C4 |
| Hall | C11×Dic103 ⋊ C5 |
| Sylow | C103 ⋊ C4×C11⋊C5 |
| Sylow | C11 ⋊ C5×Dic103 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊C5×D103 |
| commutator, hypocenter | C11×C103 | C4×C5 |
| Fitting, socle, cosocle | C2×C11×C103 | C2×C5 |
| prime radical | C2×C11⋊C5×C103 | C2 |
| LCS | G ▷ C11×C103 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4532 |
742 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22660, 10);